Our main argument consists of two steps, which we refer in the analogy to [1]}
as the decomposition step and the composition step.
In this section, we present the former,
which is analogous to that for plane trees given in [1]};
this step is also closely related to comb structure results presented in [3]}, [4]}.
As the decomposition step follows closely [1]} and the arguments are analogous,
we present the main ideas and refer the reader to [1]} for further details.
